Xiaowang Zhang

A Tableau Algorithm for Handling Inconsistency in OWL

In Semantic Web, the knowledge sources usually contain inconsistency because they are constantly changing and from different view points. As is well known, as based on the description logic, OWL is lack of the ability of tolerating inconsistent or incomplete data. Recently, the research in handling inconsistency in OWL becomes more and more important. In this paper, we present a paraconsistent OWL called quasi-classical OWL to handle inconsistency with holding important inference rules such as modus tollens, modus ponens, and disjunctive syllogism. We propose a terminable, sound and complete tableau algorithm to implement paraconsistent reasoning in quasi-classical OWL. In comparison with other approaches to handle inconsistency in OWL, our approach enhances the ability of reasoning by integrating paraconsistent reasoning with important classical inference rules.

On the Power of SPARQL in Expressing Navigational Queries

This work is supported by the project of Research Foundation Flanders (FWO) under grant G.0489.10N.

Walk logic as a framework for path query languages on graph databases

Motivated by the current interest in languages for expressing path queries to graph databases, this paper proposes to investigate Walk Logic (WL): the extension of first-order logic on finite graphs with the possibility to explicitly quantify over walks. WL can serve as a unifying framework for path query languages. To support this claim, WL is compared in expressive power with various established query languages for graphs, such as first-order logic extended with reachability; the monadic second-order logic of graphs; hybrid computation tree logic; and regular path queries. WL also serves as a framework to investigate the following natural questions: Is quantifying over walks more powerful than quantifying over paths (walks without repeating nodes) only? Is quantifying over infinite walks more powerful than quantifying over finite walks only? WL model checking is decidable, but determining the precise complexity remains an open problem.

On the Primitivity of Operators in SPARQL

The paper studies the primitivity of the basic operators UNION, AND, OPTIONAL, FILTER, and SELECT, as they are used in the SPARQL query language. The question of whether one operator can be expressed in terms of the other operators is answered in detail. It turns out that only AND is non-primitive. These results are shown to be insensitive to the choice of semantics for filter conditions (three-valued or two-valued). It is also shown that these two semantics can simulate each other.

Towards a paradoxical description logic for the semantic web

As a vision for the future of the Web, the Semantic Web is an open, constantly changing and collaborative environment. Hence it is reasonable to expect that knowledge sources in the Semantic Web contain noise and inaccuracies. However, as the logical foundation of Ontology Web Language in the Semantic Web, description logics fail to tolerate inconsistent information. The study of inconsistency handling in description logics is an important issue in the Semantic Web. One major approach to inconsistency handling is based on so-called paraconsistent reasoning, in which standard semantics is refined so that inconsistencies can be tolerated. Four-valued description logics are not satisfactory for the Semantic Web in that its reasoning is a bit far from standard semantics. In this paper, we present a paraconsistent description logic called paradoxical description logic, which is based on a three-valued semantics. Compared to existing paraconsistent description logics, our approach is more suitable for dealing with inconsistent ontologies in that paraconsistent reasoning under our semantics provides a better approximation to the standard reasoning. An important result in this paper is that we propose a sound and complete tableau for paradoxical description logics.

An argumentation framework for description logic ontology reasoning and management

This paper presents an argumentation framework for reasoning and management in (inconsistent or incoherent) description logic ontologies which contain conflicts. First, a new argumentation framework obtained by combining Besnard and Hunter’s framework with binary argumentation is introduced to frame the inner relation over axioms in an ontology. A dialogue mechanism, based on this framework, is then presented to derive meaningful consequences from inconsistent ontologies. Three novel operators are developed to repair those axioms or assertions which cause inconsistency or incoherency of ontologies by using this framework. Within this framework, an inconsistency is neither directly assigned a contradictory value nor roughly removed but further analyzed and evaluated. Because of this, reasoning within it satisfies some important logical properties such as consistency-preserving and justifiability. Moreover, it provides an alternative scenario for maintaining consistency and coherency of ontologies with giving consideration to both semantics and syntax. Thus the repaired results by using the proposed framework not only keep the closer semantics but also preserve the syntactic structure of original ontologies.

Tableau-based Forgetting in ALC Ontologies

In this paper, we propose two new approaches to forgetting for ALC based on the well-known tableau algorithm. The first approach computes the result of forgetting by rolling up tableaux, and also provides a decision algorithm for the existence of forgetting in ALC. When the result of forgetting does not exist, we provide an incremental method for computing approximations of forgetting. This second approach uses variable substitution to refine approximations of forgetting and eventually obtain the result of forgetting. This approach is capable of preserving structural information of the original ontologies enabling readability and comparison. As both approaches are based on the tableau algorithm, their implementations can make use of the mechanisms and optimization techniques of existing description logic reasoners.

Context-Free Path Queries on RDF Graphs

Navigational graph queries are an important class of queries that can extract implicit binary relations over the nodes of input graphs. Most of the navigational query languages used in the RDF community, e.g. property paths in W3C SPARQL 1.1 and nested regular expressions in nSPARQL, are based on the regular expressions. It is known that regular expressions have limited expressivity; for instance, some natural queries, like same generation-queries, are not expressible with regular expressions. To overcome this limitation, in this paper, we present cfSPARQL, an extension of SPARQL query language equipped with context-free grammars. The cfSPARQL language is strictly more expressive than property paths and nested expressions. The additional expressivity can be used for modelling graph similarities, graph summarization and ontology alignment. Despite the increasing expressivity, we show that cfSPARQL still enjoys a low computational complexity and can be evaluated efficiently.

Inconsistency-tolerant reasoning with OWL DL

The Web Ontology Language (OWL) is a family of description logic based ontology languages for the Semantic Web and gives well defined meaning to web accessible information and services. The study of inconsistency-tolerant reasoning with description logic knowledge bases is especially important for the Semantic Web since knowledge is not always perfect within it. An important challenge is strengthening the inference power of inconsistency-tolerant reasoning because it is normally impossible for paraconsistent logics to obey all important properties of inference together. This paper presents a non-classical DL called quasi-classical description logic (QCDL) to tolerate inconsistency in OWL DL which is a most important sublanguage of OWL supporting those users who want the maximum expressiveness while retaining computational completeness (i.e., all conclusions are guaranteed to be computable) and decidability (i.e., all computations terminate in finite time). Instead of blocking those inference rules, we validate them conditionally and partially, under which more useful information can still be inferred when inconsistency occurs. This new non-classical DL possesses several important properties as well as its paraconsistency in DL, but it does not bring any extra complexity in worst case. Finally, a transformation-based algorithm is proposed to reduce reasoning problems in QCDL to those in DL so that existing OWL DL reasoners can be used to implement inconsistency-tolerant reasoning. Based on this algorithm, a prototype OWL DL paraconsistent reasoner called PROSE is implemented. Preliminary experiments show that PROSE produces more intuitive results for inconsistent knowledge bases than other systems in general.

Argumentation-Based reasoning with inconsistent knowledge bases

In this paper, we present an argumentation-based approach to dealing with inconsistency occurring in knowledge bases We investigate several important logical properties of such an argumentation-based entailment relation and show its promising advantages in paraconsistent reasoning for inconsistent knowledge bases Moreover, two basic inference problems, namely, satisfiability of concepts and query entailment, are discussed under our semantics We provide a workable example in order to show the justifiability of the argumentation-based semantics.